For those that use ice machines in the fridge, do you find that it's an experience akin to using a slot machine? I mean, how many tries does it take to get that "money cube" that's just the perfect size and shape?

Using the ice tray is more like Blackjack, in my opinion. You have at least some degree of control over size and shape, but there is always an X factor at play that can alter the results (i.e a disturbance in the freezer that causes weird dents and jagged edges or small nasty floaties that get trapped in the cube, rendering it unchewable).